An Improvement of the Approximation of the Ruin Probability in a Risk Process

Title & Authors
An Improvement of the Approximation of the Ruin Probability in a Risk Process
Lee, Hye-Sun; Choi, Seung-Kyoung; Lee, Eui-Yong;

Abstract
In this paper, a continuous-time risk process in an insurance business is considered, where the premium rate is constant and the claim process forms a compound Poisson process. We say that a ruin occurs if the surplus of the risk process becomes negative. It is practically impossible to calculate analytically the ruin probability because the theoretical formula of the ruin probability contains the recursive convolutions and infinite sum. Hence, many authors have suggested approximation formulas of the ruin probability. We introduce a new approximation formula of the ruin probability which extends the well-known De Vylder`s and exponential approximation formulas. We compare our approximation formula with the existing ones and show numerically that our approximation formula gives closer values to the true ruin probability in most cases.
Keywords
Surplus process;Poisson process;risk model;run probability;approximation formula;
Language
Korean
Cited by
1.
이단계 보험요율의 복합 포아송 위험 모형의 파산 확률,송미정;이지연;

Communications for Statistical Applications and Methods, 2011. vol.18. 4, pp.433-443
2.
보험상품 파산확률의 새로운 근사방법,권청아;최승경;이의용;

Journal of the Korean Data and Information Science Society, 2014. vol.25. 1, pp.1-10
1.
New approximations of the ruin probability in a continuous time surplus process, Journal of the Korean Data and Information Science Society, 2014, 25, 1, 1
2.
Ruin Probability in a Compound Poisson Risk Model with a Two-Step Premium Rule, Communications for Statistical Applications and Methods, 2011, 18, 4, 433
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